Quad Element MIMO Antenna for C, X, Ku, and Ka-Band Applications

This article presents a quad-element MIMO antenna designed for multiband operation. The prototype of the design is fabricated and utilizes a vector network analyzer (VNA-AV3672D) to measure the S-parameters. The proposed antenna is capable of operating across three broad frequency bands: 3–15.5 GHz, encompassing the C band (4–8 GHz), X band (8–12.4 GHz), and a significant portion of the Ku band (12.4–15.5 GHz). Additionally, it covers two mm-wave bands, specifically 26.4–34.3 GHz and 36.1–48.9 GHz, which corresponds to 86% of the Ka-band (27–40 GHz). To enhance its performance, the design incorporates a partial ground plane and a top patch featuring a dual-sided reverse 3-stage stair and a straight stick symmetrically placed at the bottom. The introduction of a defected ground structure (DGS) on the ground plane serves to provide a wideband response. The DGS on the ground plane plays a crucial role in improving the electromagnetic interaction between the grounding surface and the top patch, contributing to the wideband characteristics of the antenna. The dimensions of the proposed MIMO antenna are 31.7 mm × 31.7 mm × 1.6 mm. Furthermore, the article delves into the assessment of various performance metrics related to antenna diversity, such as ECC, DG, TARC, MEG, CCL, and channel capacity, with corresponding values of 0.11, 8.87 dB, −6.6 dB, ±3 dB, 0.32 bits/sec/Hz, and 18.44 bits/sec/Hz, respectively. Additionally, the equivalent circuit analysis of the MIMO system is explored in the article. It’s worth noting that the measured results exhibit a strong level of agreement with the simulated results, indicating the reliability of the proposed design. The MIMO antenna’s ability to exhibit multiband response, good diversity performance, and consistent channel capacity across various frequency bands renders it highly suitable for integration into multi-band wireless devices. The developed MIMO system should be applicable on n77/n78/n79 5G NR (3.3–5 GHz); WLAN (4.9–5.725 GHz); Wi-Fi (5.15–5.85 GHz); LTE5537.5 (5.15–5.925 GHz); WiMAX (5.25–5.85 GHz); WLAN (5.725–5.875 GHz); long-distance radio telecommunication (4–8 GHz; C-band); satellite, radar, space communications and terrestrial broadband (8–12 GHz; X-band); and various satellite communications (27–40 GHz; Ka-band).


Introduction
Multiple input multiple output (MIMO) antenna technology is an indispensable option for wireless transmissions to meet more data needs and increase spectral efficiency.MIMO antenna configurations for 4G will also be an important system for enabling 5G [1].This 5 G communication must promote two frequency bands: the sub-6 GHz band and the mm-wave band.Focused fast transmission, shorter latency, and increased bit rate are achievable in mm-wave bands due to spectrum commitment.However, mm-wave communication experiences congestion and loss.Therefore, there should be diversified integrated antenna architectures that can provide a good frequency band [2].Implementation of these systems seems difficult due to antenna dimensions and less separation of antennas that generally operate in the microwave band [3].The proposed MIMO design in [4] has four antennas out of which two elements are operating at 3.46 GHz and the other two at 17 GHz.In this design, no elements are operating in the mm-wave 5G band.In [5], a quad-element inverted F-shaped antenna and a planar-connected array with a dimension of 100 mm × 60 mm × 0.76 mm are presented.This design has been fabricated on an RO-4350 substrate, and the proposed structure has an operating frequency of 2.1 GHz and 12.5 GHz.In [6,7], multi-layer MIMO antenna systems have been introduced with three elements and five elements.The design covers the mm-wave 5G band, but both fail to cover 5G sub-6 GHz and WLAN bands.The literature [8] consists of an eight-element MIMO antenna system in which four elements operate in the 2.4-5.6 GHz band and the other four in the 23-30 GHz frequency band.In this design, the defected ground structure is implemented to lessen the mutual coupling among elements.In [9], an eight-element integrated MIMO antenna for sub-6 GHz 5G band and mm-wave band has been proposed.Out of the eight elements, four elements operate in the sub-6 GHz 5G band (i.e., 2.38-4.13GHz and 5.04-6.12GHz), and the other four elements operate in the mm-wave band (i.e., 22.28-29.28GHz).The antenna design presented in [10][11][12] works in both the sub-6 GHz 5G band and mm-wave band; however, they do not cover the WLAN/Wi-Fi band.A miniaturized four-port MIMO antenna system has been developed in [13] for sub-6 GHz 5G band and WLAN applications.The introduced design has been operating at frequencies 2.6, 3.5, 4.8, and 5.8 GHz.A dual-band dual-port high isolation tridentshaped MIMO antenna system with an operating frequency band from 2.99 to 3.61 GHz and 4.53 to 4.92 GHz has been proposed in [14], which is operating in the sub-6 GHz 5G band only and doesn't cover the mm-wave band.The literature reported in [15,16] operated a dual frequency band under the sub-6 GHz band and the operating frequency was 3.4-3.6,4.76-5.04,and 3.95-4.04GHz, respectively.On the other end, the literature reported in [17][18][19] only covers the mm-wave 5G band, which is a bandwidth of 1.23 GHz at 28 GHz and 1.06 GHz at 38 GHz, 26-30 GHz, 36-41.5 GHz, 26.65-29.2GHz, and 36.95-39.05GHz, respectively.Additionally, the literature [20] consists of a flower-shaped radiating patch where two rectangular-shaped slots in the ground plane provide a wide band of 2.83-14.0GHz.In [21], a lotus-shaped radiating element with DGS in-ground and the addition of slits provides a 5G: n77/n78 wireless band with higher isolation (i.e., >16 dB).This article consists of three sections.The first section covers the details of antenna geometry.The second section covers the detailed analysis of different diversity characteristics parameters like ECC, DG, MEG i − MEG j , TARC, CCL, and CC.The operating bands investigated by this structure are 3-15.5GHz, 26.4-34.3GHz, and 36.1-48.9GHz, which are referred to as OFB1, OFB2, and OFB3, respectively.The minimum port isolation and ECC over the bands OFB1, OFB2, and OFB3 are observed as (15.1 dB, 0.11), (22 dB, 0.035), and (22.37 dB, 0.04), respectively.The third section provides a detailed analysis of simulated time-domain analysis in two different orientations, which are face to face (FTF) and side by side (STS).The fourth section covers the conclusion.In this study, all the simulation results are obtained from CST studio suite 2021.Computational work was conducted by MATLAB R2015a and the analysis and plotting by Origin 8.5 Pro.In all operating bands, the measured values provide good agreement with respect to the simulations.

Antenna Geometry
The proposed antenna element has a dual-side three-stage stair and a straight stick on the top of the stair.The partial ground plane has a small rectangle microstrip line just beneath the feed line.The introduction of a DGS on the ground plane serves to provide a wideband response.The DGS on the ground plane plays a crucial role in improving the electromagnetic interaction between the grounding surface and the top patch, contributing to the wideband characteristics of the antenna [22].This DGS firstly functions as an extender of the antenna's current path, thereby mitigating the resonant frequency of the antenna at its fundamental mode.Secondly, it acts as a suppressor of surface currents, thereby ameliorating isolation within the frequency bands spanning OFB1, OFB2, and OFB3.The proposed DGS approach maintains a diminished influence on the antenna's intrinsic impedance characteristics, primarily since the supplementary current pathways are realized through the judicious etching of coupling slots on the ground plane.In this design, the straight stick is a 50-ohm microstrip feed line.The design is fabricated on an FR4 substrate having a thickness of 1.6 mm with a dielectric constant of 4.4, a loss tangent of 0.02, and a copper layer thickness of 35 um.
The size of the single-element antenna is 14.7 mm × 12 mm × 1.6 mm.In this design, the following design variables are considered, which are "a", "b", "c" and "d".For optimized performance of the antenna, the design variables a, b, c, and d are considered as 1.5 mm, 2.1 mm, 3 mm, and 2.3 mm, respectively.The top and bottom views of the proposed antenna element are shown in Figures 1a and 1b, respectively.The simulated reflection coefficient is depicted in Figure 1c, where the antenna structure with a partial ground plane provides an excellent result in comparison to a structure with a full ground plane.
Furthermore, the conceptual equivalent circuit model for the proposed antenna was developed (Figure 2a).The initial approximate values for the lumped components were defined from the CST simulated antenna input impedance (Zin), and the equivalent lumped circuit parameters were then optimized using Keysight advanced design system (ADS) simulations [23].In this article, eight RLC tank circuits are connected in series due to having eight adjacent resonant frequencies overlapping with each other (Figure 1c).Note that the addition of the series capacitor Cn and inductor Ln to the RLC circuits is necessary to correctly produce the imaginary part of the antenna input impedance [24,25].

Antenna Geometry
The proposed antenna element has a dual-side three-stage stair and a straight stick on the top of the stair.The partial ground plane has a small rectangle microstrip line just beneath the feed line.The introduction of a DGS on the ground plane serves to provide a wideband response.The DGS on the ground plane plays a crucial role in improving the electromagnetic interaction between the grounding surface and the top patch, contributing to the wideband characteristics of the antenna [22].This DGS firstly functions as an extender of the antenna's current path, thereby mitigating the resonant frequency of the antenna at its fundamental mode.Secondly, it acts as a suppressor of surface currents, thereby ameliorating isolation within the frequency bands spanning OFB1, OFB2, and OFB3.The proposed DGS approach maintains a diminished influence on the antenna's intrinsic impedance characteristics, primarily since the supplementary current pathways are realized through the judicious etching of coupling slots on the ground plane.In this design, the straight stick is a 50-ohm microstrip feed line.The design is fabricated on an FR4 substrate having a thickness of 1.6 mm with a dielectric constant of 4.4, a loss tangent of 0.02, and a copper layer thickness of 35 um.
The size of the single-element antenna is 14.7 mm × 12 mm × 1.6 mm.In this design, the following design variables are considered, which are "a", "b", "c" and "d".For optimized performance of the antenna, the design variables a, b, c, and d are considered as 1.5 mm, 2.1 mm, 3 mm, and 2.3 mm, respectively.The top and bottom views of the proposed antenna element are shown in Figure 1a and 1b, respectively.The simulated reflection coefficient is depicted in Figure 1c, where the antenna structure with a partial ground plane provides an excellent result in comparison to a structure with a full ground plane.Furthermore, the conceptual equivalent circuit model for the proposed antenna was developed (Figure 2a).The initial approximate values for the lumped components were defined from the CST simulated antenna input impedance (Zin), and the equivalent lumped circuit parameters were then optimized using Keysight advanced design system (ADS) simulations [23].In this article, eight RLC tank circuits are connected in series due to having eight adjacent resonant frequencies overlapping with each other (Figure 1c).Note that the addition of the series capacitor Cn and inductor Ln to the RLC circuits is necessary to correctly produce the imaginary part of the antenna input impedance [24,25].
(a) The real (resistive part) and imaginary (reactance part) parts of the input impedance of the proposed MIMO antenna system are depicted in Figure 2. Figure 2b represents the real part of input impedance, obtained from CST and ADS simulation, whereas Figure 2c represents the imaginary part.Here, the proposed antenna shows good matching with the coaxial cable within all operating frequency bands.
developed (Figure 2a).The initial approximate values for the lumped components were defined from the CST simulated antenna input impedance (Zin), and the equivalent lumped circuit parameters were then optimized using Keysight advanced design system (ADS) simulations [23].In this article, eight RLC tank circuits are connected in series due to having eight adjacent resonant frequencies overlapping with each other (Figure 1c).Note that the addition of the series capacitor Cn and inductor Ln to the RLC circuits is necessary to correctly produce the imaginary part of the antenna input impedance [24,25].The real (resistive part) and imaginary (reactance part) parts of the input impedance of the proposed MIMO antenna system are depicted in Figure 2. Figure 2b represents the real part of input impedance, obtained from CST and ADS simulation, whereas Figure 2c represents the imaginary part.Here, the proposed antenna shows good matching with the The developed MIMO antenna covers a 37-40 GHz frequency band, which has been reported in [34][35][36].This also covers the FR2 bands above 6 GHz for 5G applications, which are n258/n259/n261 (24.25-29.5 GHz) and n260 (37-43.5 GHz) [37][38][39][40][41][42][43][44].

Antenna Operating Principle
The interfacial current distributions at a frequency of 11.1 GHz, 31.6 GHz, 37.8 GHz, and 46.7 GHz are illustrated in Figures 3a, 3b, 3c and 3d respectively.In all cases, the minimum surface currents are observed over the edges of the patch with a null point (cross-marked i.e., 'X').In Figure 3a-d the null points near the perimeter of the patch are found as 3, 9, 11, and 14, respectively.In order to find the resonance frequency, the number of null points plays a vital role.

Proposed MIMO Antenna
Embedding multiple antennas into the same antenna system is seen as a promising solution, which can improve both the system's channel capacity and the communication link's quality.The MIMO systems provide a technique in which multiple independent channels send and receive data concurrently in the same radio channel.In the MIMO system, antennas at each end of the communications circuit are combined to minimize errors, optimize data speed, and improve the capacity of radio transmissions by enabling data to travel over many signal paths at the same time.It also improves the radio link capacity to attain the multipath propagation.
The proposed quad-element MIMO antenna system is illustrated in Figure 4.The size of MIMO is 31.7 mm × 31.7 mm.In this MIMO system, the port direction of any one of the antenna is kept perpendicular to every other port direction, and the placement of antenna elements is also symmetrical to one another.Both the propertiesʹ symmetrical arrangement of elements and the orthogonality of ports lead to providing low ECC and better port isolation.Additionally, to achieve the common ground plane of the proposed MIMO system, four satire-step microstrip lines originating from each end of the rectangular microstrip line, which is present just beneath the ports in the ground plane, are connected to one common square strip.The creation of a common ground plane in this article is responsible for improving capacitance and inductance, leading to improved efficiency and gain of the MIMO antenna system.The design variable "spc" indicates the distance between two adjacent patches.In this article, "spc" is considered as 5 mm for the minimum isolation of 15 dB in the OFB1 band.
The fabricated MIMO system top and bottom views are depicted in Figure 5a and 5b, respectively.Considering the 'm' number of null points that exist over the perimeter of the patch, then the guided wavelength (λ g ) can be expressed as where L is the perimeter of the patch.In this article, L = 10 * d + 6 * c, which will be calculated as 47.4 mm.The resonance frequency can be calculated using Equation (2).
where V l is the velocity of light, L e f f is the effective length, and ∈ e f f is effective permittivity.These values can be determined using Equations ( 3) and (4).
Sensors 2023, 23, 8563 7 of 20 where, W f is feed line width, h is substrate thickness, and r is the dielectric constant of the substrate.For m = 3, 9, 11, and 14, the resonance frequency can be determined using Equation ( 2), and the obtained values are 10.4 GHz, 31.2GHz, 38.1 GHz, and 48.5 GHz, respectively, which are nearer to the simulated resonance frequency.

Proposed MIMO Antenna
Embedding multiple antennas into the same antenna system is seen as a promising solution, which can improve both the system's channel capacity and the communication link's quality.The MIMO systems provide a technique in which multiple independent channels send and receive data concurrently in the same radio channel.In the MIMO system, antennas at each end of the communications circuit are combined to minimize errors, optimize data speed, and improve the capacity of radio transmissions by enabling data to travel over many signal paths at the same time.It also improves the radio link capacity to attain the multipath propagation.
The proposed quad-element MIMO antenna system is illustrated in Figure 4.The size of MIMO is 31.7 mm × 31.7 mm.In this MIMO system, the port direction of any one of the antenna is kept perpendicular to every other port direction, and the placement of antenna elements is also symmetrical to one another.Both the properties' symmetrical arrangement of elements and the orthogonality of ports lead to providing low ECC and better port isolation.Additionally, to achieve the common ground plane of the proposed MIMO system, four satire-step microstrip lines originating from each end of the rectangular microstrip line, which is present just beneath the ports in the ground plane, are connected to one common square strip.The creation of a common ground plane in this article is responsible for improving capacitance and inductance, leading to improved efficiency and gain of the MIMO antenna system.The design variable "spc" indicates the distance between two adjacent patches.In this article, "spc" is considered as 5 mm for the minimum isolation of 15 dB in the OFB1 band.

MIMO Performance of the Proposed Antenna
The MIMO performance of the proposed antenna system is investigated in terms of S-parameter, ECC, DG, radiation pattern, efficiency, gain, MEG, TARC, CCL, and CC.The measured −10 dB impedance bandwidth of the proposed MIMO antenna system are 3-

MIMO Performance of the Proposed Antenna
The MIMO performance of the proposed antenna system is investigated in terms of S-parameter, ECC, DG, radiation pattern, efficiency, gain, MEG, TARC, CCL, and CC.The measured −10 dB impedance bandwidth of the proposed MIMO antenna system are 3-15.5GHz (% bandwidth of 116.27), 26.4-34.3GHz (% bandwidth of 32.45), and 36.1-48.9GHz (% bandwidth of 32.74).Over the entire frequency bands in OFB1, OFB2, and OFB3 the simulated minimum values of port isolation are 15.7 dB, 23.2 dB, and 23.2 dB, respectively; however, the measured minimum values of port isolation are 15 dB, 22 dB, and 22.3 dB, respectively.The simulated and measured S-parameter is depicted in Figure 6a.The envelope correlation coefficient (ρ i,j ) can be used for assessing the diversity efficiency of the MIMO antenna system.
The value of the ECC that is closest to zero implies that the MIMO antenna system has strong isolation and excellent diversity gain.Equation ( 5) [45] is used to calculate the measured ECC for a MIMO antenna system in this work.
where, → M i (θ, ϕ) indicates the 3D radiation pattern when antenna 'i' is excited, and → M j (θ, ϕ) indicates the 3D radiation pattern when antenna 'j' is excited.The solid angle is denoted by the symbol Ω.
The degree of the improvement of the MIMO system is determined by diversity gain (DG).ECC can acquire the DG [46] calculation using Equation (6).
The simulated and measured ECC and DG over the frequency bands OFB1, OFB2, and OFB3 are depicted in Figure 6b.
The simulated ECC and DG over the frequency bands OFB1, OFB2, and OFB3 are better than (0.213, 8.87 dB), (0.002, 9.89 dB), and (0.017, 9.91 dB), respectively, whereas the measured ECC and DG over the frequency bands OFB1, OFB2, and OFB3 are better than (0.1, 7.86 dB), (0.034, 9.97 dB), (0.04, 9.82 dB), respectively.The value of the ECC that is closest to zero implies that the MIMO antenna system has strong isolation and excellent diversity gain.Equation ( 5) [45] is used to calculate the measured ECC for a MIMO antenna system in this work.
where,  ⃗ ,  indicates the 3D radiation pattern when antenna 'i' is excited, and  ⃗ ,  indicates the 3D radiation pattern when antenna 'j' is excited.The solid angle is denoted by the symbol Ω.
The degree of the improvement of the MIMO system is determined by diversity gain (DG).ECC can acquire the DG [46] calculation using Equation (6).
Based on the observations, it is discovered that the radiation patterns of (Ant1, Ant3) and (Ant2, Ant4) are complementary to each other in the XZ plane.Such complementary radiation pattern qualities enable a low value of ECC between antennas and are also useful in producing self-isolated MIMO antenna systems.In Figure 8, the total efficiency and gain of Ant1 is illustrated.The simulated average efficiency and gain of Ant1 over the frequency bands OFB1, OFB2, and OFB3 are (49.1%,1.76 dB), (58.2%, 4.65 dB), and (50.5%, 5.07 dB), respectively, whereas the measured average efficiency and gain over the frequency bands OFB1, OFB2, and OFB3 are (44.3%,1.54 dB), (48.1%, 4.42 dB), and (44.9%, 4.85 dB), respectively.The mean effective gain (MEG) is a key measure for characterizing the performance of MIMO diversity.It compares the power received by the isotropic antenna to the power gained by the diversity antenna in a fade environment.The MEG of i th element of the MIMO system can be evaluated using Equation ( 7) [47].
where N is the number of elements in the MIMO system.The typical value of MEG i − MEG j should be less than 3 dB for a good MIMO antenna.The simulated and measured values of MEG i over the frequency bands OFB1, OFB2, and OFB3 are depicted in Figure 9a.The value of MEG i − MEG j for distinct values of i and j are computed, where i = j, 1 ≤ i ≤ 4 and 1 ≤ j ≤ 4. The maximum simulated values of MEG i − MEG j over the frequency bands OFB1, OFB2, and OFB3 are 0.05 dB, 0.03 dB, and 0.082 dB, respectively; however, the maximum measured values of MEG i − MEG j over the frequency bands OFB1, OFB2, and OFB3 are 0.16 dB, 0.25 dB, and 0.2 dB, respectively, which promises a good MIMO antenna in investigated operating bands.An additional fundamental diversity attribute measure that may be used to assess MIMO performance is CCL, which shows the greatest rate at which data can be delivered TARC is characterized as the square root of the overall reflected power divided by overall incident power.TARC provides a valid estimation of MIMO antenna efficiency since it contains information about the mutual coupling effect.The TARC for the N unit MIMO antenna setup can be computed using Equation ( 8) [48].
The value of TARC is calculated with the assumption of θ k−1 = 0 0 , 30 0 , 45 0 , 60 0 (where 1 ≤ k ≤ 4 and k is an integer).For a better performance in investigated bands, the TARC should be from 0 to 1 and the ideal value of TARC should be less than −10 dB.In this article, the simulated and measured TARC at θ k−1 = 0 0 , 30 0 , 45 0 , 60 0 over the frequency ranges OFB1, OFB2, and OFB3 are below or about −10 dB except for the frequency band 12-14 GHz (in this band average, TARC is −6.9 dB).The simulated and measured TARC values are illustrated in Figure 9b.
An additional fundamental diversity attribute measure that may be used to assess MIMO performance is CCL, which shows the greatest rate at which data can be delivered without experiencing significant losses.Equation ( 9) [49,50] can be utilized to calculate CCL.The CCL ought to be below 0.4 bps/Hz throughout the operating frequency spectrum for the best MIMO antenna.Here, the greatest CCL (simulated and measured) value over the frequency ranges OFB1, OFB2, and OFB3 is less than 0.3 bps/Hz, indicating a strong candidate for use on the desired band.Figure 10a shows a CCL versus frequency plot. where

Simulated Time-Domain Analysis
Since the proposed antenna is wideband in nature, it is important to check its time domain characterization.Important time domain characteristics like group delay, phase response, and isolation analysis by keeping the antenna in face-to-face (FTF) and side-toside (STS) orientation are studied.The two similar antennas are placed in two different configurations maintaining 300 mm, which are depicted in Figure 11.Ergodic channel capacity (CC), which is determined under the presumption of zero ECC among the transmitting antennas, is the most efficient diversity characteristics metric for a MIMO system.Equation ( 10) is used to evaluate the channel matrix "H".
where H iid is a 4 × 4 matrix whose elemental values are independent and identically distributed complex Gaussian random variables, ρ scale,TX is the calculated 4 × 4 matrix at the transmitter end with the consideration of null ECC and 100 percent efficiency, and ρ scale,RX is the calculated 4 × 4 matrix by employing measured ECC and efficiency as explained in [51].
Further the ρ scale,RX is calculated using Equation (11).
The variables used in Equation ( 11) are ρ RX and n total , which represents ECC and total efficiencies of receiving antennas.In order to estimate the ergodic channel capacity C, Equation ( 12) [52,53] is used.
Here, the variables in Equation ( 12), H H , SNR, n T , E and I, characterize Hermitian transpose, signal-to-noise ratio, number of antennas at the transmitter side, expectation in regard to different channel realizations, and 4 × 4 identity matrix, respectively.In this article, the ideal value of CC is computed using an average of more than 10,000 Rayleigh fading realizations with a 10 dB/20 dB SNR, null ECCs, and full efficiency of antennas.

Simulated Time-Domain Analysis
Since the proposed antenna is wideband in nature, it is important to check its time domain characterization.Important time domain characteristics like group delay, phase response, and isolation analysis by keeping the antenna in face-to-face (FTF) and side-toside (STS) orientation are studied.The two similar antennas are placed in two different configurations maintaining 300 mm, which are depicted in Figure 11.

Simulated Time-Domain Analysis
Since the proposed antenna is wideband in nature, it is important to check its time domain characterization.Important time domain characteristics like group delay, phase response, and isolation analysis by keeping the antenna in face-to-face (FTF) and side-toside (STS) orientation are studied.The two similar antennas are placed in two different configurations maintaining 300 mm, which are depicted in Figure 11. Figure 12 shows the group delay (GD), magnitude of the S21, and phase of S21.From Figure 12a,b, it is clear that the group delay lies between 1010 and 1085 ps; however, the S21 dB was below −75 dB over bandwidths OFB1, OFB2, and OFB3.The S21 phase is shown in Figure 12c-e, showing the linear features within all the desired wideband operations in both FTF and STS layouts.Figure 12 shows the group delay (GD), magnitude of the S21, and phase of S21.From Figure 12a,b, it is clear that the group delay lies between 1010 and 1085 ps; however, the S21 dB was below −75 dB over bandwidths OFB1, OFB2, and OFB3.The S21 phase is shown in Figure 12c-e, showing the linear features within all the desired wideband operations in both FTF and STS layouts.Figure 12 shows the group delay (GD), magnitude of the S21, and phase of S21.From Figure 12a,b, it is clear that the group delay lies between 1010 and 1085 ps; however, the S21 dB was below −75 dB over bandwidths OFB1, OFB2, and OFB3.The S21 phase is shown in Figure 12c-e, showing the linear features within all the desired wideband operations in both FTF and STS layouts.In order to discuss the time-domain analysis, the fidelity factor of antenna and system fidelity factor play a crucial role.The antenna fidelity factor (FF) is obtained by calculating the cross-correlation of the radiated E-field and the input signal; however, the system In order to discuss the time-domain analysis, the fidelity factor of antenna and system fidelity factor play a crucial role.The antenna fidelity factor (FF) is obtained by calculating the cross-correlation of the radiated E-field and the input signal; however, the system fidelity factor (SFF) is calculated by the cross-correlation between the transmitted pulse and the received pulse.The simulated value of FF and SFF are calculated in two different orientations (face to face and side by side), by keeping the proposed antenna 300 mm apart.Here the Gaussian sine pulse is given as input to the Tx port in order to find the FF and SFF.The obtained value of FF and SFF is presented in Table 2.The antenna's compact dimensions impact its transient behavior, and the level of pulse distortion is considered acceptable (SFF > 0.5 [54,55]), which is suitable for use in impulse-type UWB systems.
Table 3 indicates the recently reported literature comparison, in which the literature [8,9,13] covers the WLAN band and only [8] covers the n77/n78/n79 5G NR band.Here the proposed MIMO covers n77/n78/n79 5G NR band, WLAN, Wi-Fi, and wide band mm-Wave.None of the reported antennas in Table 1 calculates the CC, which is essential for investigating MIMO performance.The proposed MIMO system computed the CC in operating bands, which is quite suitable for investigated bands.

Figure 2 .
Figure 2. Proposed single antenna element: (a) Equivalent lumped circuit model (b) Impedance real part, and (c) Impedance imaginary part.

Figure 2 .
Figure 2. Proposed single antenna element: (a) Equivalent lumped circuit model (b) Impedance real part, and (c) Impedance imaginary part.

15 . 5
GHz (% bandwidth of 116.27), 26.4-34.3GHz (% bandwidth of 32.45), and 36.1-48.9GHz (% bandwidth of 32.74).Over the entire frequency bands in OFB1, OFB2, and OFB3 the simulated minimum values of port isolation are 15.7 dB, 23.2 dB, and 23.2 dB, respectively; however, the measured minimum values of port isolation are 15 dB, 22 dB, and 22.3 dB, respectively.The simulated and measured S-parameter is depicted in Figure 6a.The envelope correlation coefficient ( , ) can be used for assessing the diversity efficiency of the MIMO antenna system.

Figure 7 Figure 6 .
Figure 7 depicts the simulated and measured two-dimensional (2-D) radiation patterns of Ant1-Ant4 at the frequencies 11.1 GHz, 31.6 GHz, 37.8 GHz, and 46.8 GHz in the XZ plane.Sensors 2023, 23, x FOR PEER REVIEW 9 of 21

Figure 8 .
Figure 8. Simulated and measured gain-efficiency versus frequency plot.Figure 8. Simulated and measured gain-efficiency versus frequency plot.

Figure 11 .
Figure 11.Simulated time-domain analysis in the layout: (a) Face to Face and (b) Side to Side.

Figure 11 .
Figure 11.Simulated time-domain analysis in the layout: (a) Face to Face and (b) Side to Side.

Figure 11 .
Figure 11.Simulated time-domain analysis in the layout: (a) Face to Face and (b) Side to Side.

Table 2 .
Simulated value of FF and SFF.

Table 3 .
Comparison table of recently reported articles.

Table 3 .
Cont. → free space wavelength (mm) at lowest operating frequency band RAD→ Radiation efficiency AVG→ Average ECC over entire operating band.